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Chapter 2 History of rheology and Newton
Chapter 2 History of rheology and Newton 2.1
Introduction
It seems as if investigations concerning the rheology of lubricants, the relationship between deformation and stresses, were not performed until the industrial revolution made it necessary to distinguish between different viscosity grades used for different applications [Dowson 19791. Before that time mainly the boundary lubrication properties of vegetable oils and animal fats were used to decrease friction and wear and to reduce stick-slip. As far back as 1684, Hooke [Hooke 16841 seems to have recognized the importance of proper lubrication and in Philosophize Naturalis Principia Mathematica [Newton 16861 Sir Isaac Newton introduced the term defectus lubricitatis which today would be called internal friction or viscosity. In section IX of book I1 of the Principia, Newton treats Circular Motion of Fluids and opens with a hypothesis containing a statement today described as Newton’s law of viscous flow: The resistance arising from the want of lubricity in the parts of a fluid, is, other things being equal, proportional to the velocity with which the parts of the fluid are separated from one another.... Newton used the words defectus Jubricitatis but did not mention the word viscosity despite the fact that it had been used for more than two hundred years. The first time the word viscous was used in a written text was in 1400 (Lafranc), and the word viscosity was used in a text in 1425 (Arderne). In both cases the use of the word was in connection with the description of sticky body fluids. The word viscosity as such has its roots in mistletoe berries which contain a very sticky substance called viscin which in turn forms the main constituent of bird-lime. Bird-lime was traditionally used as a sticky substance to spread on twigs to catch birds. The word viscosity has its roots in the Greek word for mistletoe and it has come to the English language via the Old French viscosite or medeival Latin viscositas. The use of the word in physics seems not to have been in evidence until the eighteenth century. In 1786 the military and hydraulics engineer Du Buat (1734-1809) noted that temperature had an influence on the resistance to fluid flow (viscosity), but it took another fifty years before Navier introduced the coefficient of viscosity into the equations of motion for liquids. When Newton in the Principia postulated a viscosity, it was not for the study of the lubrication of bearings. He was interested in explaining the motion of the planets around the sun, and tried to get the rotational speed for each planet from the flow velocity of a vortex motion around the rotating sun. His studies showed that a fluid obeying his hypothesis would form a vortex around a rotating sphere with a time of rotation proportional to the square of the distance 13
14
CHAPTER 2. HISTORY OF RHEOLOGY AND NEWTON
to the centre of motion, whereas the planets moving around Jupiter and those revolving around the sun had times of rotation proportional to the radius to a power 1.5. He thereby demonstrated that vortex motion of a viscous fluid pervading the universe could not explain the observed motions of the planets. There is no evidence to show that Newton considered the important application of viscous flow theory to fluid film lubrication.
2.2
Early viscosity measurements
A number of measuring instruments which could compare the fluidity of lubricants was developed in Europe and North America in the second half of the nineteenth century. It could perhaps be assumed that the development of such instruments was a consequence of scientific studies in the 1880’s which confirmed the extreme importance of viscosity in the physical process of fluid film lubrication. An examination of the literature, however, shows that this is not completely true, although the 1880’s not only accelerated the studies of viscosity but also provided a sound basis for the lubrication process. This is clearly developed in History of Tribology where Professor Dowson describes the different stages in viscosity measurements through the last centuries [Dowson 19791. Most of the facts in this chapter have been taken from that book. The use of steam engines had already shown the limitations of oxidation prone and thermally unstable vegetable and animal oils as lubricants when Charles Dolfuss addressed the Soci6t6 Industrielle de Mulhouse on 29 June 1831. He described and demonstrated an instrument consisting of a vessel with a small hole in its base. The vessel was filled with the fluid to be tested. By noting the time needed for a certain volume of the fluid to leave the vessel Dolfuss derived an index for its liquidity. The inventor called the instrument a viscom6tre and it was widely acclaimed as a most useful instrument [Forbes 19581. In the early 1840’s in Paris, a professor in the medical schools studied the passage of blood through fine capillaries by investigating the flow of water through the bores of thermometer tubes. Jean M.L. Poiseuille thus determined the viscosity by means of measurement of the flow through thin tubes. This is treated in detail in chapter 3.2. Initially, horizontal tubes were used, and this arrangement for lubrication studies was used in the viscometer introduced by Slotte 1881. If the horizontal tube viscometer is made longer to increase the accuracy of the measurement, it becomes fragile and difficult to contain in a constant temperature chamber. Stone (1915) therefore introduced a vertical tube viscometer which can be seen as the forerunner to the modern U-tube viscometer. In parallel with the ever-increasing refinement of the long capillary viscometer, various forms of robust short-tube viscometers were introduced into industry in the 1880’s. Three, the Redwood, the Saybolt, and the Engler, developed in England, the USA, and Germany, became particularly well known and can still be seen in lubricant-testing laboratories. While they all differ in detail these commercial viscometers employ the same principle. The test fluid is placed in a central, open cup and filled to a definite depth while being surrounded by a water or oil bath to provide some degree of temperature control. The centre of the base of the cup contains a small orifice or a short length of capillary tube controlled by a simple valve. The time required for a certain volume of the liquid to leave the container gives a measure of the viscosity in arbitrary units known as Redwood seconds, Saybolt seconds or Engler degrees. It can be seen at once that these instruments were essentially developments of the Dolfuss viscometer.
2.2. EARLY VISCOSITY MEASUREMENTS
15
The Engler viscometer was the first to receive official recognition, having been adopted for comparison of lubricants by a German railway committee as early as 1884. Engler described the viscometer in a paper in 1885, although it was later subjected to a number of minor changes designed to standardize dimensions and thus to improve the comparability between different individual viscometers. The Engler degree ( E ) was the ratio of the times taken for 200 cm3 (12.2 in3) of the test fluid and water to flow from the cup. The kinematic viscosity, ( u ), defined as the ratio of the absolute viscosity (v ) to the density ( p ) of the lubricant, could then be calculated from an empirical relationship between u and E . Mr Boverton Redwood designed his viscometer in 1885 and in 1886 he gave a full account of the instrument. It was a modification of an instrument developed by a chemist at Price’s Patent Candle Company in Battersea by the name of C. Rumble. At the same lecture in 1886 Redwood also displayed an instrument developed for the same purpose by an Inspector of the Standard Oil Company of New York, Mr G.M. Saybolt. Redwood used agate as the material for the jet and expressed the viscosity of lubricants as a percentage of that of rapeseed oil at 15.6”C (60°F). He appears to have done this deliberately to enable those engineers using the new mineral oils to appreciate the viscosity of their new lubricants against a background of something within their experience. The Redwood second was the time of efflux of a given quantity of lubricant and the instrument achieved wide acceptance in England. Like the Engler viscometer it was going to be subjected to a long period of standardization and in due course the National Physical Laboratory was to issue certificates to instruments which met the agreed specifications. An empirical equation enabled Redwood seconds to be converted to kinematic viscosity. In the Saybolt viscometer the volume of efflux was measured within the cup itself. The instrument was clearly available in the mid-1880’s for it was exhibited by Redwood in England, but a full description did not emerge until Herschel 1918 published a standard set of dimensions agreed by Saybolt. A later agreement between Saybolt and the Bureau of Standards was adopted by the American Society of Testing Materials (ASTM) and the standard Saybolt universal viscometer became as familiar and well established in the United States as the Redwood viscometer was in England and the Engler viscometer in Germany. Since all these instruments enable viscosity to be calculated from empirical equations related to the characteristics of the form of the viscometer there are relationships between the basic units of measurement for the Redwood and Saybolt seconds and the Engler degrees. In this section attention has been focused upon the early history of the accurate measurement of viscosity, the most important single property of most lubricants. It should be remembered, however, that it was not until the 1880’s that scientists and engineers developed a sound appreciation of the importance of viscosity. Prior to that time ‘fluidity’ was discussed and several other properties were measured and related to lubricating ability. In particular, density or specific gravity was often the basis of comparison. Finally, it should not be forgotten that ‘viscosity’ and the ‘coefficient of viscocity’ were not firmly defined until Maxwell 1860 discussed the matter in his Bakerian Lecture the year after Colonel Edwin L. Drake struck oil in Titusville.
CHAPTER 2. HISTORY OF RHEOLOGY AND NEWTON
16
2.3
Conclusion
During the last 130 years a number of instruments has been developed which measure flow properties both on static as well as dynamic liquid systems. By assuming simplified mathematical relations between deformation rate and stresses it is possible to develop rheometers to measure the different parameters, but hidden behind the measurement principles are always some assumptions about the liquid behaviour. All rheometers assume for instance that the liquids to be tested are wetting the surfaces of the viscometer, so the velocity of the liquid at the instrument walls is the same as the velocity of the walls. In many of the viscometers available on the market today the shear stress and shear strain rates are not constant throughout the volume of the tested fluid. This means that the measured values are not directly giving the shear stress and the shear strain rate, but the behaviour of the liquid is assumed to follow Newton’s law and measurements are made of some mean value properties like volume flow or force. This means that the local shear strain rate - shear stress relationship is not measured, and if the measurement is only made at one stress level it is not possible to determine if the liquid studied has non-Newtonian properties or not. Some of the viscometers treated in chapter 3 are of this type, for instance the capillary tube viscometer, the falling ball viscometer, and the flat channel viscometer. If the capillary tube viscometer and the flat channel viscometer can be charged with different pressure gradients, non-Newtonian behaviour can be found, but it is still not possible to determine the actual shear stress - shear strain rate curve without making some assumptions and performing some curve fitting. The only way to measure the local properties of a fluid is to make sure that the whole volume of the liquid is subjected to the same stress, with the same pressure and temperature prevailing. Two viscometers with these properties are treated in chapter 6.
Bibliography [Dowson 19791 Dowson, D., “History of Tribology”, Longman Group Limited, London, 1979. [Forbes 19581 Forbes, R.J., “Petroleum” in “A History of Technology”, Volume V, The Late Nineteenth Century c. 1850-1900, pp. 102-123, Clarendon Press Oxford, 1958. [Hooke 16841
Hooke, R., see Gunther, R.T., “Early Science in Oxford”, Vols VI and VII, “The Life and Work of Robert Hooke”, Oxford, 1930.
[Newton 16861 Newton, I., “Philosophiae Naturales Principia Mathematica”, Imprimature S. Pepys, Reg. SOC.Praeses, 5 Julii 1686, Londonii.
17
Introduction
It seems as if investigations concerning the rheology of lubricants, the relationship between deformation and stresses, were not performed until the industrial revolution made it necessary to distinguish between different viscosity grades used for different applications [Dowson 19791. Before that time mainly the boundary lubrication properties of vegetable oils and animal fats were used to decrease friction and wear and to reduce stick-slip. As far back as 1684, Hooke [Hooke 16841 seems to have recognized the importance of proper lubrication and in Philosophize Naturalis Principia Mathematica [Newton 16861 Sir Isaac Newton introduced the term defectus lubricitatis which today would be called internal friction or viscosity. In section IX of book I1 of the Principia, Newton treats Circular Motion of Fluids and opens with a hypothesis containing a statement today described as Newton’s law of viscous flow: The resistance arising from the want of lubricity in the parts of a fluid, is, other things being equal, proportional to the velocity with which the parts of the fluid are separated from one another.... Newton used the words defectus Jubricitatis but did not mention the word viscosity despite the fact that it had been used for more than two hundred years. The first time the word viscous was used in a written text was in 1400 (Lafranc), and the word viscosity was used in a text in 1425 (Arderne). In both cases the use of the word was in connection with the description of sticky body fluids. The word viscosity as such has its roots in mistletoe berries which contain a very sticky substance called viscin which in turn forms the main constituent of bird-lime. Bird-lime was traditionally used as a sticky substance to spread on twigs to catch birds. The word viscosity has its roots in the Greek word for mistletoe and it has come to the English language via the Old French viscosite or medeival Latin viscositas. The use of the word in physics seems not to have been in evidence until the eighteenth century. In 1786 the military and hydraulics engineer Du Buat (1734-1809) noted that temperature had an influence on the resistance to fluid flow (viscosity), but it took another fifty years before Navier introduced the coefficient of viscosity into the equations of motion for liquids. When Newton in the Principia postulated a viscosity, it was not for the study of the lubrication of bearings. He was interested in explaining the motion of the planets around the sun, and tried to get the rotational speed for each planet from the flow velocity of a vortex motion around the rotating sun. His studies showed that a fluid obeying his hypothesis would form a vortex around a rotating sphere with a time of rotation proportional to the square of the distance 13
14
CHAPTER 2. HISTORY OF RHEOLOGY AND NEWTON
to the centre of motion, whereas the planets moving around Jupiter and those revolving around the sun had times of rotation proportional to the radius to a power 1.5. He thereby demonstrated that vortex motion of a viscous fluid pervading the universe could not explain the observed motions of the planets. There is no evidence to show that Newton considered the important application of viscous flow theory to fluid film lubrication.
2.2
Early viscosity measurements
A number of measuring instruments which could compare the fluidity of lubricants was developed in Europe and North America in the second half of the nineteenth century. It could perhaps be assumed that the development of such instruments was a consequence of scientific studies in the 1880’s which confirmed the extreme importance of viscosity in the physical process of fluid film lubrication. An examination of the literature, however, shows that this is not completely true, although the 1880’s not only accelerated the studies of viscosity but also provided a sound basis for the lubrication process. This is clearly developed in History of Tribology where Professor Dowson describes the different stages in viscosity measurements through the last centuries [Dowson 19791. Most of the facts in this chapter have been taken from that book. The use of steam engines had already shown the limitations of oxidation prone and thermally unstable vegetable and animal oils as lubricants when Charles Dolfuss addressed the Soci6t6 Industrielle de Mulhouse on 29 June 1831. He described and demonstrated an instrument consisting of a vessel with a small hole in its base. The vessel was filled with the fluid to be tested. By noting the time needed for a certain volume of the fluid to leave the vessel Dolfuss derived an index for its liquidity. The inventor called the instrument a viscom6tre and it was widely acclaimed as a most useful instrument [Forbes 19581. In the early 1840’s in Paris, a professor in the medical schools studied the passage of blood through fine capillaries by investigating the flow of water through the bores of thermometer tubes. Jean M.L. Poiseuille thus determined the viscosity by means of measurement of the flow through thin tubes. This is treated in detail in chapter 3.2. Initially, horizontal tubes were used, and this arrangement for lubrication studies was used in the viscometer introduced by Slotte 1881. If the horizontal tube viscometer is made longer to increase the accuracy of the measurement, it becomes fragile and difficult to contain in a constant temperature chamber. Stone (1915) therefore introduced a vertical tube viscometer which can be seen as the forerunner to the modern U-tube viscometer. In parallel with the ever-increasing refinement of the long capillary viscometer, various forms of robust short-tube viscometers were introduced into industry in the 1880’s. Three, the Redwood, the Saybolt, and the Engler, developed in England, the USA, and Germany, became particularly well known and can still be seen in lubricant-testing laboratories. While they all differ in detail these commercial viscometers employ the same principle. The test fluid is placed in a central, open cup and filled to a definite depth while being surrounded by a water or oil bath to provide some degree of temperature control. The centre of the base of the cup contains a small orifice or a short length of capillary tube controlled by a simple valve. The time required for a certain volume of the liquid to leave the container gives a measure of the viscosity in arbitrary units known as Redwood seconds, Saybolt seconds or Engler degrees. It can be seen at once that these instruments were essentially developments of the Dolfuss viscometer.
2.2. EARLY VISCOSITY MEASUREMENTS
15
The Engler viscometer was the first to receive official recognition, having been adopted for comparison of lubricants by a German railway committee as early as 1884. Engler described the viscometer in a paper in 1885, although it was later subjected to a number of minor changes designed to standardize dimensions and thus to improve the comparability between different individual viscometers. The Engler degree ( E ) was the ratio of the times taken for 200 cm3 (12.2 in3) of the test fluid and water to flow from the cup. The kinematic viscosity, ( u ), defined as the ratio of the absolute viscosity (v ) to the density ( p ) of the lubricant, could then be calculated from an empirical relationship between u and E . Mr Boverton Redwood designed his viscometer in 1885 and in 1886 he gave a full account of the instrument. It was a modification of an instrument developed by a chemist at Price’s Patent Candle Company in Battersea by the name of C. Rumble. At the same lecture in 1886 Redwood also displayed an instrument developed for the same purpose by an Inspector of the Standard Oil Company of New York, Mr G.M. Saybolt. Redwood used agate as the material for the jet and expressed the viscosity of lubricants as a percentage of that of rapeseed oil at 15.6”C (60°F). He appears to have done this deliberately to enable those engineers using the new mineral oils to appreciate the viscosity of their new lubricants against a background of something within their experience. The Redwood second was the time of efflux of a given quantity of lubricant and the instrument achieved wide acceptance in England. Like the Engler viscometer it was going to be subjected to a long period of standardization and in due course the National Physical Laboratory was to issue certificates to instruments which met the agreed specifications. An empirical equation enabled Redwood seconds to be converted to kinematic viscosity. In the Saybolt viscometer the volume of efflux was measured within the cup itself. The instrument was clearly available in the mid-1880’s for it was exhibited by Redwood in England, but a full description did not emerge until Herschel 1918 published a standard set of dimensions agreed by Saybolt. A later agreement between Saybolt and the Bureau of Standards was adopted by the American Society of Testing Materials (ASTM) and the standard Saybolt universal viscometer became as familiar and well established in the United States as the Redwood viscometer was in England and the Engler viscometer in Germany. Since all these instruments enable viscosity to be calculated from empirical equations related to the characteristics of the form of the viscometer there are relationships between the basic units of measurement for the Redwood and Saybolt seconds and the Engler degrees. In this section attention has been focused upon the early history of the accurate measurement of viscosity, the most important single property of most lubricants. It should be remembered, however, that it was not until the 1880’s that scientists and engineers developed a sound appreciation of the importance of viscosity. Prior to that time ‘fluidity’ was discussed and several other properties were measured and related to lubricating ability. In particular, density or specific gravity was often the basis of comparison. Finally, it should not be forgotten that ‘viscosity’ and the ‘coefficient of viscocity’ were not firmly defined until Maxwell 1860 discussed the matter in his Bakerian Lecture the year after Colonel Edwin L. Drake struck oil in Titusville.
CHAPTER 2. HISTORY OF RHEOLOGY AND NEWTON
16
2.3
Conclusion
During the last 130 years a number of instruments has been developed which measure flow properties both on static as well as dynamic liquid systems. By assuming simplified mathematical relations between deformation rate and stresses it is possible to develop rheometers to measure the different parameters, but hidden behind the measurement principles are always some assumptions about the liquid behaviour. All rheometers assume for instance that the liquids to be tested are wetting the surfaces of the viscometer, so the velocity of the liquid at the instrument walls is the same as the velocity of the walls. In many of the viscometers available on the market today the shear stress and shear strain rates are not constant throughout the volume of the tested fluid. This means that the measured values are not directly giving the shear stress and the shear strain rate, but the behaviour of the liquid is assumed to follow Newton’s law and measurements are made of some mean value properties like volume flow or force. This means that the local shear strain rate - shear stress relationship is not measured, and if the measurement is only made at one stress level it is not possible to determine if the liquid studied has non-Newtonian properties or not. Some of the viscometers treated in chapter 3 are of this type, for instance the capillary tube viscometer, the falling ball viscometer, and the flat channel viscometer. If the capillary tube viscometer and the flat channel viscometer can be charged with different pressure gradients, non-Newtonian behaviour can be found, but it is still not possible to determine the actual shear stress - shear strain rate curve without making some assumptions and performing some curve fitting. The only way to measure the local properties of a fluid is to make sure that the whole volume of the liquid is subjected to the same stress, with the same pressure and temperature prevailing. Two viscometers with these properties are treated in chapter 6.
Bibliography [Dowson 19791 Dowson, D., “History of Tribology”, Longman Group Limited, London, 1979. [Forbes 19581 Forbes, R.J., “Petroleum” in “A History of Technology”, Volume V, The Late Nineteenth Century c. 1850-1900, pp. 102-123, Clarendon Press Oxford, 1958. [Hooke 16841
Hooke, R., see Gunther, R.T., “Early Science in Oxford”, Vols VI and VII, “The Life and Work of Robert Hooke”, Oxford, 1930.
[Newton 16861 Newton, I., “Philosophiae Naturales Principia Mathematica”, Imprimature S. Pepys, Reg. SOC.Praeses, 5 Julii 1686, Londonii.
17